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On the Existence of Rainbow 4-Term Arithmetic Progressions


For infinitely many natural numbers n, we construct 4-colorings of [n]  =  {1, 2, ..., n}, with equinumerous color classes, that contain no 4-term arithmetic progression whose elements are colored in distinct colors. This result solves an open problem of Jungić et al. (Comb Probab Comput 12:599–620, 2003) Axenovich and Fon-der-Flaass (Electron J Comb 11:R1, 2004).

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Correspondence to Radoš Radoičić.

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Conlon, D., Jungić, V. & Radoičić, R. On the Existence of Rainbow 4-Term Arithmetic Progressions. Graphs and Combinatorics 23, 249–254 (2007).

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  • Arithmetic Progression
  • Distinct Color
  • Color Class
  • Acta Arith
  • Consecutive Integer